上海师范大学学报(自然科学版)
上海師範大學學報(自然科學版)
상해사범대학학보(자연과학판)
JOURNAL OF SHANGHAI TEACHERS UNIVERSITY(NATURAL SCIENCES)
2009年
2期
111-117
,共7页
单恺婷%江峰%匡蛟勋%田红炯
單愷婷%江峰%劻蛟勛%田紅炯
단개정%강봉%광교훈%전홍형
比例尺微分方程%稳定性%时滞微分方程
比例呎微分方程%穩定性%時滯微分方程
비례척미분방정%은정성%시체미분방정
pantograph differential equation%stability%delay differential equation
主要研究了多延时非线性比例尺方程理论解及数值解的稳定性质Y'(t)=f(t,y(t),y( λd t)t…,y(λd t)),其中f:R×CN×…×CN→CN,y:R→CN,0< λd<…< λ1<1.获得了比例尺微分方程稳定及渐近稳定的充分条件, 同时研究了隐式欧拉方法的稳定性质.
主要研究瞭多延時非線性比例呎方程理論解及數值解的穩定性質Y'(t)=f(t,y(t),y( λd t)t…,y(λd t)),其中f:R×CN×…×CN→CN,y:R→CN,0< λd<…< λ1<1.穫得瞭比例呎微分方程穩定及漸近穩定的充分條件, 同時研究瞭隱式歐拉方法的穩定性質.
주요연구료다연시비선성비례척방정이론해급수치해적은정성질Y'(t)=f(t,y(t),y( λd t)t…,y(λd t)),기중f:R×CN×…×CN→CN,y:R→CN,0< λd<…< λ1<1.획득료비례척미분방정은정급점근은정적충분조건, 동시연구료은식구랍방법적은정성질.
This paper deals with the stability properties of the analytic and numerical solutions of nonlinear systems of pantograph differential equations with many delays. Sufficient conditions for the trivial solutions of the pantograph differential equations to be stable and asymptotically stable are derived. We also focus on the corresponding numerical stability properties of the implicit Euler method solving the underlying differential equation.
